Regression Discontinuity (RD)¶

RD2_1f¶

Assignment	Clustering Level	Treatment Assignment	Treatment Level	Cluster Effect
blocked	2	individual	1	fixed

[1]:

from pypowerup import effect_size, sample_size, power

[2]:

# effect size, i.e., minimum detectable effect sizes (MDES)
effect_size(design = "rd2_1f", n=55, J=20, r21=0.5, g=1, design_effect=2.75)

[2]:

0.19828457764454652

[3]:

# sample_size, i.e., minimum required samples sizes (MRSS) for level 2 units
sample_size(design = "rd2_1f", es=0.19828457764454652, n=55, r21=0.5, g=1, design_effect=2.75)

[3]:

20.0

[4]:

# power
power(design = "rd2_1f", es=0.19828457764454652, n=55, r21=0.5, J=20, g=1, design_effect=2.75)

[4]:

0.8000010686602212

Parameters	`effect_size`	`sample_size`	`power`
design	✓	✓	✓
es		✓	✓
n	✓	✓	✓
J	✓		✓
power	✓	✓
alpha	✓	✓	✓
two_tailed	✓	✓	✓
p	✓	✓	✓
r21	✓	✓	✓
g	✓	✓	✓
design_effect	✓	✓	✓

RD2_1r¶

Assignment	Clustering Level	Treatment Assignment	Treatment Level	Cluster Effect
blocked	2	individual	1	random

[5]:

# effect size, i.e., minimum detectable effect sizes (MDES)
effect_size(design = "rd2_1r", n=50, J=40, r21=0.5, g=1, r2t2=0.1, omega2=0.2, rho2= 0.15, design_effect=2.75)

[5]:

0.15782962225367275

[6]:

# sample_size, i.e., minimum required samples sizes (MRSS) for level 2 units
sample_size(design = "rd2_1r", es=0.15782962225367275, n=50,r21=0.5, g=1,
          r2t2=0.1, omega2=0.2, rho2= 0.15, design_effect=2.75)

[6]:

40.0

[7]:

# power
power(design = "rd2_1r", es=0.15782962225367275, n=50, J=40, r21=0.5, g=1,
      r2t2=0.1, omega2=0.2, rho2= 0.15, design_effect=2.75)

[7]:

0.8000090684884187

Parameters	`effect_size`	`sample_size`	`power`
design	✓	✓	✓
es		✓	✓
n	✓	✓	✓
J	✓		✓
power	✓	✓
alpha	✓	✓	✓
two_tailed	✓	✓	✓
p	✓	✓	✓
r21	✓	✓	✓
rho2	✓	✓	✓
r2t2	✓	✓	✓
g	✓	✓	✓
design_effect	✓	✓	✓

RDC_2r¶

Assignment	Clustering Level	Treatment Assignment	Treatment Level	Cluster Effect
simple	2	cluster	2	random

[8]:

# effect size, i.e., minimum detectable effect sizes (MDES)
effect_size(design = "rdc_2r", rho2=0.15, r21=0.5, r22=0.5, g=1, n=55, J=179, design_effect=2.75)

[8]:

0.20086870136611698

[9]:

# sample_size, i.e., minimum required samples sizes (MRSS) for level 2 units
sample_size(design = "rdc_2r", es=0.20086870136611698, rho2=0.15, r21=0.5,
            r22=0.5, g=1, n=55, design_effect=2.75)

[9]:

179.0

[10]:

# power
power(design = "rdc_2r", es=0.20086870136611698, rho2=0.15, r21=0.5,
            r22=0.5, g=1, n=55, J=179, design_effect=2.75)

[10]:

0.8000017574724924

Parameters	`effect_size`	`sample_size`	`power`
design	✓	✓	✓
es		✓	✓
n	✓	✓	✓
J	✓		✓
power	✓	✓
alpha	✓	✓	✓
two_tailed	✓	✓	✓
p	✓	✓	✓
r21	✓	✓	✓
rho2	✓	✓	✓
r22	✓	✓	✓
g	✓	✓	✓
design_effect	✓	✓	✓

RDC_3r¶

Assignment	Clustering Level	Treatment Assignment	Treatment Level	Cluster Effect
simple	3	cluster	3	random

[11]:

# effect size, i.e., minimum detectable effect sizes (MDES)
effect_size(design = "rdc_3r", rho3=0.15, rho2=0.15, r21=0.5, r22=0.5,
            r23=0.5,  g=1, n=18, J=3, K=230, design_effect=2.75)

[11]:

0.20079075638849297

[12]:

# sample_size, i.e., minimum required samples sizes (MRSS) for level 2 units
sample_size(design = "rdc_3r", es=0.20079075638849297, rho3=0.15, rho2=0.15, r21=0.5, r22=0.5,
            r23=0.5,  g=1, n=18, J=3, design_effect=2.75)

[12]:

230.0

[13]:

# power
power(design = "rdc_3r", es=0.20079075638849297, rho3=0.15, rho2=0.15, r21=0.5, r22=0.5,
            r23=0.5,  g=1, n=18, J=3, K=230, design_effect=2.75)

[13]:

0.8000015459112233

Parameters	`effect_size`	`sample_size`	`power`
design	✓	✓	✓
es		✓	✓
n	✓	✓	✓
J	✓	✓	✓
K	✓		✓
power	✓	✓
alpha	✓	✓	✓
two_tailed	✓	✓	✓
p	✓	✓	✓
r21	✓	✓	✓
rho2	✓	✓	✓
r22	✓	✓	✓
rho3	✓	✓	✓
r23	✓	✓	✓
g	✓	✓	✓
design_effect	✓	✓	✓

RD2_3f¶

Assignment	Clustering Level	Treatment Assignment	Treatment Level	Cluster Effect
blocked	3	cluster	2	fixed

[14]:

# effect size, i.e., minimum detectable effect sizes (MDES)
effect_size(design = "rd3_2f", rho2=0.15, r21=0.5, r22=0.5, g=0, n=18, J=3, K=71, design_effect=2.75)

[14]:

0.20131125779908843

[15]:

# sample_size, i.e., minimum required samples sizes (MRSS) for level 3 units
sample_size(design = "rd3_2f", es=0.20131125779908843, rho2=0.15, r21=0.5, r22=0.5, g=0,
            n=18, J=3, design_effect=2.75)

[15]:

71.0

[16]:

# power
power(design = "rd3_2f", es=0.20131125779908843, rho2=0.15, r21=0.5, r22=0.5, g=0,
            n=18, J=3, K=71, design_effect=2.75)

[16]:

0.8000020062425997

Parameters	`effect_size`	`sample_size`	`power`
design	✓	✓	✓
es		✓	✓
n	✓	✓	✓
J	✓	✓	✓
K	✓		✓
power	✓	✓
alpha	✓	✓	✓
two_tailed	✓	✓	✓
p	✓	✓	✓
r21	✓	✓	✓
rho2	✓	✓	✓
r22	✓	✓	✓
g	✓	✓	✓
design_effect	✓	✓	✓

RD2_3r¶

Assignment	Clustering Level	Treatment Assignment	Treatment Level	Cluster Effect
blocked	3	cluster	2	random

[17]:

# effect size, i.e., minimum detectable effect sizes (MDES)
effect_size(design = "rdc_3r", rho3=0.15, rho2=0.15, r21=0.5, r22=0.5, r23=0.5,
            g=1, n=18, J=3, K=230, design_effect=2.75)

[17]:

0.20079075638849297

[18]:

# sample_size, i.e., minimum required samples sizes (MRSS) for level 3 units
sample_size(design = "rdc_3r", es=0.20079075638849297, rho3=0.15, rho2=0.15, r21=0.5, r22=0.5, r23=0.5,
            g=1, n=18, J=3, design_effect=2.75)

[18]:

230.0

[19]:

# power
power(design = "rdc_3r", es=0.20079075638849297, rho3=0.15, rho2=0.15, r21=0.5, r22=0.5, r23=0.5,
            g=1, n=18, J=3, K=230, design_effect=2.75)

[19]:

0.8000015459112233

Parameters	`effect_size`	`sample_size`	`power`
design	✓	✓	✓
es		✓	✓
n	✓	✓	✓
J	✓	✓	✓
K	✓		✓
power	✓	✓
alpha	✓	✓	✓
two_tailed	✓	✓	✓
p	✓	✓	✓
r21	✓	✓	✓
rho2	✓	✓	✓
r22	✓	✓	✓
rho3	✓	✓	✓
r2t3	✓	✓	✓
omega3	✓	✓	✓
g	✓	✓	✓
design_effect	✓	✓	✓